Instrumentation Tutorial

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Field Wiring and Noise Considerations for Analog Signals

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Overview

Unfortunately, measuring analog signals with a data acquisition device is not always as simple as wiring the signal source leads to the data acquisition device. Knowledge of the nature of the sig

source, a suitable configuration of the data acquisition device, and an appropriate cabling scheme may be required to produce accurate and noise-free measurements. Figure 1 shows a block

diagram of a typical data acquisition system. The integrity of the acquired data depends upon the entire analog signal path In order to cover a wide variety of applications, most data acquisitiondevices provide some flexibility in their analog input stage configuration. The price of this flexibility is, however, some confusion as to the proper applications of the various input configurations an

their relative merits. This note helps clarify the types o f input configurations available on data acquisition devices, explains how the user should choose and use the configuration best for the

application, and discusses interference noise pick up mechanisms and how to minimize interference noise by proper cabling and shielding. An understanding of the types of signal sources and

measurement systems is a prerequisite to application of good measurement techniques, so we will begin by discussing the same.

Table of Contents

Types of Signal Sources and Measurement Systems

Measuring Grounded Signal Sources

Measuring Floating (Nonreferenced) Sources

Minimizing Noise Coupling in the Interconnects

Balanced Systems

Solving Noise Problems in Measurement Setups

Signal Processing Techniques for Noise Reduction

References

Types of Signal Sources and Measurement Systems

By far the most common electrical equivalent produced by signal conditioning circuitry associated with sensors is in the form of voltage. Transformation to other electrical phenomena such as

current and frequency may be encountered in cases where the signal is to be carried over long cabling in harsh environments. Since in virtually all cases the transformed signal is ultimately

converted back into a voltage signal before measurement, it is important to understand the voltage signal source.

Remember that a voltage signal is measured as the potential difference across two points. This is depicted in Figure 2.

Voltage Signal Source and Measurement System ModelFigure 2.

A voltage source can be grouped into one of two categoriesgrounded or ungrounded (floating). Similarly, a measurement system can be grouped into one of two categoriesgrounded or

ground-referenced, and ungrounded (floating).

Grounded or Ground-Referenced Signal Source

A grounded source is one in which the voltage signal is referenced to the building system ground. The most common example of a grounded source is any common plug-in instrument that does

explicitly its output signal. Figure 3 shows a grounded signal source.float

Grounded Signal SourceFigure 3.

The grounds of two grounded signal sources will generally not be at the same potential. The difference in ground potential between two instruments connected to the same building power system

typically on the order of 10 mV to 200 mV; however, the difference can be higher if power distribution circuits are not properly connected.

Ungrounded or Nonreferenced (Floating) Signal Source

A floating source is a source in which the voltage signal is not referred to an absolute reference, such as earth or building ground. Some common examples of floating signal sources are batterie

battery powered signal sources, thermocouples, transformers, isolation amplifiers, and any instrument that explicitly its output signal. A nonreferenced or floating signal source is depicted floats

Figure 4.

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Floating or Nonreferenced Signal SourceFigure 4.

Notice that neither terminal of the source is referred to the electrical outlet ground. Thus, each terminal is independent of earth.

Differential or Nonreferenced Measurement System

A differential, or nonreferenced, measurement system has neither of its inputs tied to a fixed reference such as earth or building ground. Hand-held, battery-powered instruments and data

acquisition devices with instrumentation amplifiers are examples of differential or nonreferenced measurement systems. Figure 5 depicts an implementation of an 8-channel differential

measurement system used in a typical device from National Instruments. Analog multiplexers are used in the signal path to increase the number of measurement channels while still using a sing

instrumentation amplifier. For this device, the pin labeled AI GND, the analog input ground, is the measurement system ground.

An 8-Channel Differential Measurement SystemFigure 5.

An ideal differential measurement system responds only to the potential between its two terminalsthe (+) and () inputs. Any voltage measured with respect to the instrumentationdifference

amplifier ground that is present at both amplifier inputs is referred to as a common-mode voltage. Common-mode voltage is completely rejected (not measured) by an ideal differential

measurement system. This capability is useful in rejection of noise, as unwanted noise is often introduced in the circuit making up the cabling system as common-mode voltage. Practical devices

however, have several limitations, described by parameters such as common-mode voltage range and common-mode rejection ratio (CMRR), which limit this ability to reject the common-mode

voltage.

Common-mode voltage V is defined as follows:cm

V = (V + V )/2cm

+

where V = Voltage at the noninverting terminal of the measurement system with respect to the measurement system ground, V = Voltage at the inverting terminal of the measurement system +

respect to the measurement system ground and CMRR in dB is defined as follows:

CMRR (dB) = 20 log (Differential Gain/Common-Mode Gain).

A simple circuit that illustrates the CMRR is shown in Figure 6. In this circuit, CMRR in dB is measured as 20 log V /V where V = V = V .cm out+

cm


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CMRR Measurement CircuitFigure 6.

The common-mode voltage range limits the allowable voltage swing on each input with respect to the measurement system ground. Violating this constraint results not only in measurement erro

but also in possible damage to components on the device. As the term implies, the CMRR measures the ability of a differential measurement system to reject the common-mode voltage signal. T

CMRR is a function of frequency and typically reduces with frequency. The CMRR can be optimized by using a balanced circuit. This issue is discussed in more detail later in this application note

Most data acquisition devices will specify the CMRR up to 60 Hz, the power line frequency.

Grounded or Ground-Referenced Measurement System

A grounded or ground-referenced measurement system is similar to a grounded source in that the measurement is made with respect to ground. Figure 7 depicts an 8-channel grounded

measurement system. This is also referred to as a .single-ended measurement system

An 8-Channel Ground-Referenced Single-Ended (RSE) Measurement SystemFigure 7.

A variant of the single-ended measurement technique, known as nonreferenced single-ended (NRSE), is often found in data acquisition devices. A NRSE measurement system is depicted in Fig

8.

An 8-Channel NRSE Measurement SystemFigure 8.

In an NRSE measurement system, all measurements are still made with respect to a single-node Analog Input Sense (AI SENSE), but the potential at this node can vary with respect to the

measurement system ground (AI GND). Figure 8 illustrates that a single-channel NRSE measurement system is the same as a single-channel differential measurement system.

Now that we have identified the different signal source type and measurement systems, we can discuss the proper measurement system for each type of signal source.

Measuring Grounded Signal Sources

A grounded signal source is best measured with a differential or nonreferenced measurement system. Figure 9 shows the pitfall of using a ground-referenced measurement system to measure a

grounded signal source. In this case, the measured voltage, V , is the sum of the signal voltage, V , and the potential difference, DV , that exists between the signal source ground and them s g

measurement system ground. This potential difference is generally not a DC level; thus, the result is a noisy measurement system often showing power-line frequency (60 Hz) components in the

readings. Ground-loop introduced noise may have both AC and DC components, thus introducing offset errors as well as noise in the measurements. The potential difference between the twogrounds causes a current to flow in the interconnection. This current is called ground-loop current.


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A Grounded Signal Source Measured with a Ground-Referenced System Introduces Ground LoopFigure 9.

A ground-referenced system can still be used if the signal voltage levels are high and the interconnection wiring between the source and the measurement device has a low impedance. In this

case, the signal voltage measurement is degraded by ground loop, but the degradation may be tolerable. The polarity of a grounded signal source must be carefully observed before connecting i

a ground-referenced measurement system because the signal source can be shorted to ground, thus possibly damaging the signal source. Wiring considerations are discussed in more detail lat

in this application note.

A nonreferenced measurement is provided by both the differential (DIFF) and the NRSE input configurations on a typical data acquisition device. With either of these configurations, any potentia

difference between references of the source and the measuring device appears as common-mode voltage to the measurement system and is subtracted from the measured signal. This is

illustrated in Figure 10.

A Differential Measurement System Used to Measure a Grounded Signal SourceFigure 10.

Measuring Floating (Nonreferenced) Sources

Floating signal sources can be measured with both differential and single-ended measurement systems. In the case of the differential measurement system, however, care should be taken to

ensure that the common-mode voltage level of the signal with respect to the measurement system ground remains in the common-mode input range of the measurement device.

A variety of phenomenafor example, the instrumentation amplifier input bias currentscan move the voltage level of the floating source out of the valid range of the input stage of a data

acquisition device. To anchor this voltage level to some reference, resistors are used as illustrated in Figure 11. These resistors, called bias resistors, provide a DC path from the instrumentation

amplifier inputs to the instrumentation amplifier ground. These resistors should be of a large enough value to allow the source to float with respect to the measurement reference (AI GND in the

previously described measurement system) and not load the signal source, but small enough to keep the voltage in the range of the input stage of the device. Typically, values between 10 k an

100 k work well with low-impedance sources such as thermocouples and signal conditioning module outputs. These bias resistors are connected between each lead and the measurement syst

ground.

Failure to use these resistors will result in erratic or saturated (positive full-scale or negative full-scale) readings.Warning:

If the input signal is DC-coupled, only one resistor connected from the () input to the measurement system ground is required to satisfy the bias current path requirement, but this leads to an

unbalanced system if the source impedance of the signal source is relatively high. Balanced systems are desirable from a noise immunity po int of view. Consequently, two resistors of equal

valueone for signal high (+) input and the other for signal low () input to groundshould be used if the source impedance of the signal source is high. A single bias resistor is sufficient for

low-impedance DC-coupled sources such as thermocouples. Balanced circuits are discussed further later in this application note.

If the input signal is AC-coupled, two bias resistors are required to satisfy the bias current path requirement of the instrumentation amplifier.

Resistors (10 k < R < 100 k) provide a return path to ground for instrumentation amplifier input bias currents, as shown in Figure 11. Only R2 is required for DC-coupled signal sources. For

AC-coupled sources, R1 = R2.

Floating Source and Differential Input ConfigurationFigure 11.

If the single-ended input mode is to be used, a RSE input system (Figure 12a) can be used for a floating signal source. No ground loop is created in this case. The NRSE input system (Figure 12

can also be used and is preferable from a noise pickup point of view. Floating sources do require bias resistor(s) between the AI SENSE input and the measurement system ground (AI GND) in

NRSE input configuration.


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Floating Signal Source and Single-Ended ConfigurationsFigure 12.

A graphic summary of the previous discussion is presented in Table 1.

Analog Input ConnectionsTable 1.

Bias resistors must be provided when measuring floating signal sources in DIFF and NRSE configurations. Failure to do so will result in erratic or saturated (positive full-scale or negativWarning:

full-scale) readings.

In general, a differential measurement system is preferable because it rejects not only ground loop-induced errors, but also the noise picked up in the environment to a certain degree. The

single-ended configurations, on the other hand, provide twice as many measurement channels but are justified only if the magnitude of the induced errors is smaller than the required accuracy of

the data. Single-ended input connections can be used when all input signals meet the following criteria.

Input signals are high level (greater than 1 V)

Signal cabling is short and travels through a noise-free environment or is properly shielded

All input signals can share a common reference signal at the source


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Differential connections should be used when any of the above criteria are violated.

Minimizing Noise Coupling in the Interconnects

Even when a measurement setup avoids ground loops or analog input stage saturation by following the above guidelines, the measured signal will almost inevitably include some amount of nois

or unwanted signal "picked up" from the environment. This is especially true for low-level analog signals that are amplified using the onboard amplifier that is available in many data acquisition

devices. To make matters worse, PC data acquisition boards generally have some digital input/output signals on the I/O connector. Consequently, any activity on these digital signals provided by

to the data acquisition board that travels across some length in close proximity to the low-level analog signals in the interconnecting cable itself can be a source of noise in the amplified signal. In

order to minimize noise coupling from th is and other extraneous sources, a proper cabling and shielding scheme may be necessary.

Before proceeding with a discussion of proper cabling and shielding, an understanding of the nature of the interference noise-coupling problem is required. There is no single solution to the

noise-coupling problem. Moreover, an inappropriate solution might make the problem worse.

An interference or noise-coupling problem is shown in Figure 13.

Noise-Coupling Problem Block DiagramFigure 13.

As shown in Figure 13, there are four principal noise "pick up" or coupling mechanismsconductive, capacitive, inductive, and radiative. Conductive coupling results from sharing currents from

different circuits in a common impedance. Capacitive coupling results from time-varying electric fields in the vicinity of the signal pa th. Inductive or magnetically coupled noise results from

time-varying magnetic fields in the area enclosed by the signal circuit. If the electromagnetic field source is far from the signal circuit, the electric and magnetic field coupling are considered

combined electromagnetic or radiative coupling.

Conductively Coupled Noise

Conductively coupled noise exists because wiring conductors have finite impedance. The effect of these wiring impedances must be taken into account in designing a wiring scheme. Conductive

coupling can be eliminated or minimized by breaking ground loops (if any) and providing separated ground returns for both low-level and high-level, high-power signals. A series ground-connecti

scheme resulting in conductive coupling is illustrated in Figure 14a.

If the resistance of the common return lead from A to B is 0.1 , the measured voltage from the temperature sensor would vary by 0.1 * 1 A = 100 mV, depending on whether the switch is clos

or open. This translates to 10 of error in the measurement of temperature. The circuit of Figure 14b provides separate ground returns; thus, the measured temperature sensor output does not va

as the current in the heavy load circuit is turned on and off.


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Conductively Coupled NoiseFigure 14.

Capacitive and Inductive Coupling

The analytical tool required for describing the interaction of electric and magnetic fields of the noise and signal circuits is the mathematically nontrivial Maxwells equation. For an intuitive and

qualitative understanding of these coupling channels, however, lumped circuit equivalents can be used. Figures 15 and 16 show the lumped circuit equivalent of electric and magnetic field coupl

Capacitive Coupling between the Noise Source and Signal Circuit, Modeled by the Capacitor C in the Equivalent CircuitFigure 15.ef


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Inductive Coupling between the Noise Source and Signal Circuit, Modeled by the Mutual Inductance M in the Equivalent CircuitFigure 16.

Introduction of lumped circuit equivalent models in the noise equivalent circuit handles a violation o f the two underlying assumptions of electrical circuit analysis; that is, all electric fields are

confined to the interior of capacitors, and all magnetic fields are confined to the interior of inductors.

Capacitive Coupling

The utility of the lumped circuit equivalent of coupling channels can be seen now. An electric field coupling is modeled as a capacitance between the two circuits. The equivalent capacitance C ef

directly proportional to the area of overlap and inversely proportional to the distance between the two circuits. Thus, increasing the separation or minimizing the overlap will minimize C and henef

the capacitive coupling from the noise circuit to the signal circuit. Other characteristics of capacitive coupling can be derived from the model as well. For example, the level of capacitive coupling is

directly proportional to the frequency and amplitude of the noise source and to the impedance of the receiver circuit. Thus, capacitive coupling can be reduced by reducing noise source voltage ofrequency or reducing the signal circuit impedance. The equivalent capacitance C can also be reduced by employing capacitive shielding. Capacitive shielding works by bypassing or providing

ef

another path for the induced current so it is not carried in the signal circuit. Proper capacitive shielding requires attention to both the shield location and the shield connection. The shield must be

placed between the capacitively coupled conductors and connected to ground only at the source end. Significant ground currents will be carried in the shield if it is grounded at both ends. For

example, a potential difference of 1 V between grounds can force 2 A of ground current in the shield if it has a resistance of 0.5 . Potential differences on the order of 1 V can exist between

grounds. The effect of this potentially large ground current will be explored further in the discussion of inductively coupled noise. As a general rule, conductive metal or conductive material in the

vicinity of the signal path should not be left electrically floating either, because capacitively coupled noise may be increased.

Improper Shield TerminationGround Currents Are Carried in the ShieldFigure 17.

Proper Shield TerminationNo Ground or Signal Current Flows through the ShieldFigure 18.

Inductive Coupling

As described earlier, inductive coupling results from time-varying magnetic fields in the area enclosed by the signal circuit loop. These magnetic fields are generated by currents in nearby noise

circuits. The induced voltage V in the signal circuit is given by the formula:n


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V = 2p fBACos (1)n

where f is the frequency o f the sinusoidally varying flux density, B is the rms value of the flux density, A is the area of the signal circuit loop, and is the angle between the flux density B and the

area A.

The lumped circuit equivalent model of inductive coupling is the mutual inductance M as shown in Figure 16(b). In terms of the mutual inductance M, V is given by the formula:n

V = 2p fMI (2)n n

where I is the rms value of the sinusoidal current in the noise circuit, and f is its frequency.n

Because M is directly proportional to the area of the receiver circuit loop and inversely proportional to the distance between the noise source circuit and the signal circuit, increasing the separatio

or minimizing the signal loop area will minimize the inductive coupling between the two circuits. Reducing the current I in the noise circuit or reducing its frequency can also reduce the inductiven

coupling. The flux density B from the noise circuit can also be reduced by twisting the noise source wires. Finally, magnetic shielding can be applied either to noise source or signal circuit to

minimize the coupling.

Shielding against low-frequency magnetic fields is not as easy as shielding against electric fields. The effectiveness of magnetic shielding depends on the type of materialits permeability, its

thickness, and the frequencies involved. Due to its high relative permeability, steel is much more effective than aluminum and copper as a shield for low-frequency (roughly below 100 kHz)

magnetic fields. At higher frequencies, however, a luminum and copper can be used as well. Absorption loss of copper and steel for two thicknesses is shown in Figure 19. The magnetic shielding

properties of these metals are quite ineffective at low frequencies such as those of the power line (50 to 60 Hz), which are the principal low-frequency, magnetically-coupled noise sources in most

environments. Better magnetic shields such as Mumetal can be found for low-frequency magnetic shielding, but Mumetal is very fragile and can have severe degradation of its permeability, and

hence, degradation of its effectiveness as a magnetic shield by mechanical shocks.

Absorption Loss as a Function of Frequency (from Reference 1)Figure 19.

Because of the lack of control over the noise circuit parameters and the relative difficulty of achieving magnetic shielding, reducing the signal circuit loop area is an effective way to minimize

inductive coupling. Twisted-pair wiring is beneficial because it reduces both the loop area in the signal circuit and cancels induced errors.

Formula (2) determines the effect of carrying ground-loop currents in the shield for the circuit in Figure 17. For I = 2 A; f = 60 Hz; and M = 1 H/ft for a 10-ft cable results in the following:n

V = (2)(3.142)(60)(1 10 10)(2) = 7.5 mVn

6

This noise level translates into 3.1 LSB for a 10 V range, 12-bit data acquisition system. The effectiveness of the data acquisition system is thus reduced roughly to that of a 10-bit acquisition

system.

When using an E Series device with a shielded cable in differential mode, the signal circuit loop area is minimized because each pair of signal leads is configured as a twisted pair. This is not tru

for the single-ended mode with the same device and cable because loop areas of different sizes may be formed with different channels.

Current signal sources are more immune to this type of noise than voltage signal sources because the magnetically induced voltage appears in series with the source, as shown in Figure 20. V 2

and V are inductively coupled noise sources, and V is a capacitively coupled noise source.22 c


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Circuit Model of Inductive and Capacitive Noise Voltage CouplingFigure 20.

(H. W. Ott, Noise Reduction Techniques in Electronic Systems, Wiley, 1976.)

The level of both inductive and capacitive coupling depends on the noise amplitude and the proximity of the noise source and the signal circuit. Thus, increasing separation from interfering circuit

and reducing the noise source amplitude are beneficial. Conductive coupling results from d irect contact; thus, increasing the physical separation from the noise circuit is not useful.

Radiative Coupling

Radiative coupling from radiation sources such as radio and TV broadcast stations and communication channels would not normally be considered interference sources for the low-frequency (les

than 100 kHz) bandwidth measurement systems. But high-frequency noise can be rectified and introduced into low-frequency circuits through a process called . This processaudio rectification

results from the nonlinear junctions in ICs acting as rectifiers. Simple passive R-C lowpass filters at the receiver end of long cabling can reduce audio rectification.

The ubiquitous computer terminal is a source of electric and magnetic field interference in nearby sensitive circuits. This is illustrated in Figure 21, which shows the graphs of data obtained with a

data acquisition device using a gain of 500 with the onboard programmable gain amplifier. The input signal is a short circuit at the termination block. A 0.5 m unshielded interconnecting cable wa

used between the terminal block and the device I/O connector. For differential signal connection, the channel high and channel low inputs were tied together and to the analog system ground. Fo

the single-ended connection, the channel input was tied to the analog system ground.

Noise Immunity of Differential Input Configuration Compared with that of RSE Configuration (DAQ board gain: 500; Cable: 0.5 m Unshielded; Noise Source: Computer Monitor)Figure 21.

Miscellaneous Noise Sources

Whenever motion of the interconnect cable is involved, such as in a vibrational environment, attention must be paid to the triboelectric effect, as well as to induced voltage due to the changing

magnetic flux in the signal circuit loop. The triboelectric effect is caused by the charge generated on the dielectric within the cable if it does not maintain contact with the cable conductors.

Changing magnetic flux can result from a change in the signal circuit loop area caused by motion of one or both of the conductorsjust another manifestation of inductive coupling. The solution

to avoid dangling wires and to clamp the cabling.


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In measurement circuits dealing with very low-level circuits, attention must be paid to yet another source of measurement errorthe inadvertent thermocouples formed across the junctions of

dissimilar metals. Errors due to thermocouple effects do not constitute interference type errors but are worth mentioning because they can be the cause of mysterious offsets between channels i

low-level signal measurements.

Balanced Systems

In describing the differential measurement system, it was mentioned that the CMRR is optimized in a balanced circuit. A balanced circuit is one that meets the following three criteria:

The source is balancedboth terminals of the source (signal high and signal common) have equal impedance to ground.

The cable is balancedboth conductors have equal impedance to ground.

The receiver is balancedboth terminals of the measurement end have equal impedance to ground.

Capacitive pickup is minimized in a balanced circuit because the noise voltage induced is the same on both conductors due to their equal impedances to ground and to the noise source.

Capacitive Noise Coupling Circuit ModelFigure 22.

(H.W. Ott, Noise Reduction Techniques in Electronic Systems, Wiley, 1976.)

If the circuit model of Figure 22 represented a balanced system, the following conditions would apply:

Z = Z and Z = Z1 2 c1 c2

Simple circuit analysis shows that for the balanced case V = V , the capacitively coupled voltage V appears as a common-mode signal. For the unbalanced case, that is, either Z Z or Z+ c 1 2 c1

, the capacitively coupled voltage V appears as a differential voltage, that is, V V , which cannot be rejected by an instrumentation amplifier. The higher the imbalance in the system orc2 c

+

mismatch of impedances to ground and the capacitive coupling noise source, the higher the differential component of the capacitively coupled noise will be.

A differential connection presents a balanced receiver on the data acquisition device side of the cabling, but the circuit is not balanced if either the source or the cabling is not balanced. This is

illustrated in Figure 23. The data acquisition device is configured for differential input mode at a gain of 500. The source impedance R was the same (1 k) in both the setups. The bias resistorss

used in the circuit of Figure 23b are both 100 k. The common-mode rejection is better for the circuit in Figure 23b than for Figure 23a. Figure 23c and 23d are time-domain plots of the data

obtained from configurations 23a and 23b respectively. Notice the absence of noise-frequency components with the balanced source configuration. The noise source in this setup was the compu

monitor. The balanced setup also loads the signal source with

R = R + Rg1 g2

This loading effect should not be ignored. The unbalanced setup does not load the signal source.

In a setup such as the one in Figure 23a, the imbalance in the system (mismatch in impedance to ground from the signal high and low conductors) is proportional to the source impedance R . Fos

the limiting case R = 0 , the setup in Figure 23a is also balanced, and thus less sensitive to noise.s


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Source Setup and the Acquired DataFigure 23.

Twisted pairs or shielded, twisted pairs are examples of balanced cables. Coaxial cable, on the other hand, is not balanced because the two conductors have different capacitance to ground.

Source Impedance Characteristics

Because the source impedance is important in determining capacitive noise immunity of the cabling from the source to the data acquisition system, the impedance characteristics of some of the

most common transducers are listed in Table 2.

Impedance Characteristics of TransducersTable 2.

Transducer Impedance Characteristic

Thermocouples Low (1 kohm)

Resistance Temperature Detector Low (1 kohm)

Strain Gauges Low (


13/13

Equation (4) determines the combination of the number of samples and the sampling interval to reject a specific interfering frequency by averaging. For example, for 60 Hz rejection using N cycles

3 and N = 40, we can calculate the optimal sampling rate as follows:s

T = 3 / (60 40) = 1.25 mss

Thus, averaging 40 samples acquired at a sampling interval of 1.25 ms (or 800 samples/s) will reject 60 Hz no ise from the acquired data. Similarly, averaging 80 samples acquired at 800 sample

(10 readings/s) will reject both 50 and 60 Hz frequencies. When using a lowpass digital filtering technique, such as averaging, you cannot assume that the resultant data has no DC errors such a

offsets caused by ground loops. In other words, if a no ise problem in a measurement system is resolved by averaging, the system may still have DC offset errors. The system must be verified if

absolute accuracy is critical to the measurements.

References

Ott, Henry W., . New York: John Wiley & Sons, 1976.Noise Reduction Techniques in Electronic Systems

Barnes, John R., , New Jersey: Prentice-Hall, Inc., 1987.Electronic System Design: Interference and Noise Control Techniques

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